# Q. 32^5 + 2^27 is divisible by

a) 3

b) 7

c) 10

d) 11

Correct answer: c) 10

##### Question from UPSC Prelims 2024 CSAT Paper

**Explanation:**

## 32^5 + 2^27

1) 32^5:

32 = 2^5

So, 32^5 = (2^5)^5 = 2^25

2) Now our expression is 2^25 + 2^27

3) We can factor out 2^25:

2^25 * (1 + 2^2) = 2^25 * (1 + 4) = 2^25 * 5

4) Now, let’s consider the divisibility:

c) 10: 2^25 * 5 is clearly divisible by 10, and since 2^25 * 5 = 2^24*10

The answer remains c) 10.